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📝 Derivative of a Quotient

📖 From Calculus • 3. The Derivation • 27 questions available

Practice MCQs for Derivative of a Quotient. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-13

9
Easy Questions
11
Medium Questions
7
Hard Questions

📝 Sample Questions

Q1. What is the derivative of \(f(x) = \frac{x^2}{x+1}\) using the quotient rule?

🔹 A. \(\frac{x^2 + 2x}{(x+1)^2}\)
🔹 B. \(\frac{x^2 - 2x}{(x+1)^2}\)
🔹 C. \(\frac{x^2 + 2x + 1}{(x+1)^2}\)
🔹 D. \(\frac{2x}{x+1}\)

💡 Difficulty: easy | ✅ Correct: A

Q2. Find the derivative of \(f(x) = \frac{x}{x^2 - 1}\).

🔹 A. \(\frac{-x^2 - 1}{(x^2-1)^2}\)
🔹 B. \(\frac{-x^2 + 1}{(x^2-1)^2}\)
🔹 C. \(\frac{x^2 + 1}{(x^2-1)^2}\)
🔹 D. \(\frac{-x^2 - 1}{x^2-1}\)

💡 Difficulty: medium | ✅ Correct: A

Q3. Find the derivative of \(f(x) = \frac{x^2 - 4}{x + 2}\) after simplifying.

🔹 A. \(1\)
🔹 B. \(2x\)
🔹 C. \(1 - \frac{4}{x^2}\)
🔹 D. \(\frac{2x}{x+2}\)

💡 Difficulty: hard | ✅ Correct: A

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🔗 Related Topics

📝 Approximating Roots📝 Areas and Limits📝 Continuity in Applications📝 Continuity of Compositions📝 Continuity of Inverse Functions
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